Question

prove that the points A(-2, -1) B(1, 0) C(4, 3) and d(1, 2) are vertices of a parallelogram

Answer 1

Answer:

It is a parallelogram

Step-by-step explanation:

We have

A(-2,-1)

B(1,0)

C(4,3)

D(1,2)

Now, By Distance Formula

AB² = (1+2)² + (0+1)²

= (3)² + (1)²

= 9 + 1

= 10

AB = root 10

BC² = (4-1)² + (3-0)²

= (3)² + (3)²

= 9+9

= 18

BC = root 18

CD² = (4-1)² + (3-2)²

= (3)² + (1)2

= 9 + 1

= 10

CD = root 10

DA² = (1+2)² + (2+1)²

= (3)² + (3)²

= 9 + 9

= 18

DA = root 18

We observe, here AB=CD and BC=DA

Therefore, ABCD is a parallelogram